An intersex person is typically assigned a gender at birth, but so is everyone else. Being intersex just means you aren’t biologically male or female (though I think this might also include people who have sex chromosomes that develop as though they were the other binary sex, but I’m not an expert). Most intersex people don’t typically know they are intersex, and thus they would count as cisgender so long as they identify as the gender they were assigned at birth and transgender if they do not. Thus, if someone had, say XY chromosomes, but was assigned female at birth, they would probably be cis if they identified as female.
However, trans can be a bit of a self-identifying label, and thus someone in that situation might just as well consider themselves trans. There’s a lot of different definitions for trans. Many non-binary people would consider themselves trans since they don’t identify as their assigned gender at birth.
Long story short, gender is complicated. Sex doesn’t change (put a couple asterisks here), but gender is super flexible (also asterisks here.)
There are 23 movies in the Air Bud cinematic universe. Everyone always talks about the first Air Bud. The basketball one. The dog does a trick and boops the basketball into the hoop. Whoop-de-fucking-doo. If I’m on the losing team to that, I can applaud that. That’s fine, whatever, I’d hurt my nose doing that. Cool. The rest of the team played well, too.
Now imagine being a kid on a sports team six years later. You arrive to your beach volleyball court and see you’re playing against a dog. You might think, woah, the dog is just gonna boop the ball with his nose, right? Cool fucking trick, he’s old as shit and has no new ones. Wrong. In Air Bud: Spikes Back, the fifth Air Bud movie, the eponymous Air Bud jumps up to the net and spikes a ball down on the opposing team. If I’m on the losing team to that, I fucking quit volleyball forever. There’s no going back. Your dad doesn’t ask how the game was, he saw the dog spike that shit on you on ESPN. What were you supposed to do? My fucking bad, our libero is a piece of shit who can’t dig it up from a FUCKING DOG??? Where the FUCK is our middle blocker??? Which one of you pieces of shit let’s the dog go unmarked after that??? Slam the fucking ball into him, holy shit! No wonder we lost, they were too busy laughing their asses off while we floundered to get the ball over the net! Holy fucking shit, Andre, if you set the ball up so the FUCKING DOG GETS A CHANCE TO BLOCK ME WHY THE FUCK ARE YOU THE SETTER?!? No way, there is NO WAY anyone plays volleyball on that team again. Half that team kills themselves from the ridicule after that. The other half moves across the country and changes their names and faces. That dog ruins their lives. All to win a volleyball game.